{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AYMA3WDNDY3PTPLSLGHSC2C52M","short_pith_number":"pith:AYMA3WDN","schema_version":"1.0","canonical_sha256":"06180dd86d1e36f9bd72598f21685dd316360cb75f8ac61acb018374ba482a1d","source":{"kind":"arxiv","id":"1610.06448","version":2},"attestation_state":"computed","paper":{"title":"The generalized Catalan equation in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Peter Koymans","submitted_at":"2016-10-20T14:50:16Z","abstract_excerpt":"Let $K = \\mathbb{F}_p(z_1, \\ldots, z_r)$ be a finitely generated field over $\\mathbb{F}_p$. In this article we study the generalized Catalan equation $ax^m + by^n = 1$ in $x, y \\in K$ and integers $m, n > 1$ coprime with $p$. Our main result shows that there are only finitely many solutions up to the action of Frobenius."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.06448","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-20T14:50:16Z","cross_cats_sorted":[],"title_canon_sha256":"2d42f26bcf6defd7f48fc78439afb40fbee2f133c683456b99a6b042617079d9","abstract_canon_sha256":"bfd683a96bf9d8db3d8d5d9581e613f5532111172c1ad6a027f3bae100dfc855"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:52.316097Z","signature_b64":"KDL76m6cv37BYL+BcKbiHDQgTnZvuBDwpTtfpzJx8hksTEAgxtyepugJadVShv0JYaU4GhGXQorWsWF8eHTsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06180dd86d1e36f9bd72598f21685dd316360cb75f8ac61acb018374ba482a1d","last_reissued_at":"2026-05-18T01:00:52.315562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:52.315562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The generalized Catalan equation in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Peter Koymans","submitted_at":"2016-10-20T14:50:16Z","abstract_excerpt":"Let $K = \\mathbb{F}_p(z_1, \\ldots, z_r)$ be a finitely generated field over $\\mathbb{F}_p$. In this article we study the generalized Catalan equation $ax^m + by^n = 1$ in $x, y \\in K$ and integers $m, n > 1$ coprime with $p$. Our main result shows that there are only finitely many solutions up to the action of Frobenius."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06448","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.06448","created_at":"2026-05-18T01:00:52.315658+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.06448v2","created_at":"2026-05-18T01:00:52.315658+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06448","created_at":"2026-05-18T01:00:52.315658+00:00"},{"alias_kind":"pith_short_12","alias_value":"AYMA3WDNDY3P","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AYMA3WDNDY3PTPLS","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AYMA3WDN","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AYMA3WDNDY3PTPLSLGHSC2C52M","json":"https://pith.science/pith/AYMA3WDNDY3PTPLSLGHSC2C52M.json","graph_json":"https://pith.science/api/pith-number/AYMA3WDNDY3PTPLSLGHSC2C52M/graph.json","events_json":"https://pith.science/api/pith-number/AYMA3WDNDY3PTPLSLGHSC2C52M/events.json","paper":"https://pith.science/paper/AYMA3WDN"},"agent_actions":{"view_html":"https://pith.science/pith/AYMA3WDNDY3PTPLSLGHSC2C52M","download_json":"https://pith.science/pith/AYMA3WDNDY3PTPLSLGHSC2C52M.json","view_paper":"https://pith.science/paper/AYMA3WDN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.06448&json=true","fetch_graph":"https://pith.science/api/pith-number/AYMA3WDNDY3PTPLSLGHSC2C52M/graph.json","fetch_events":"https://pith.science/api/pith-number/AYMA3WDNDY3PTPLSLGHSC2C52M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AYMA3WDNDY3PTPLSLGHSC2C52M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AYMA3WDNDY3PTPLSLGHSC2C52M/action/storage_attestation","attest_author":"https://pith.science/pith/AYMA3WDNDY3PTPLSLGHSC2C52M/action/author_attestation","sign_citation":"https://pith.science/pith/AYMA3WDNDY3PTPLSLGHSC2C52M/action/citation_signature","submit_replication":"https://pith.science/pith/AYMA3WDNDY3PTPLSLGHSC2C52M/action/replication_record"}},"created_at":"2026-05-18T01:00:52.315658+00:00","updated_at":"2026-05-18T01:00:52.315658+00:00"}